You should at least be able to visualise what the cross-sections of the surface along the coordinate axes look like. On the x-axis, for example, where y=0, f(x,y) is equal to x^3, and you surely know what the graph of that curve looks like, with a point of inflection at the origin.

From what I am understanding the critical point then should be a saddle point, am I right?

No, because there is no direction in which it is either a local maximum or a local minimum. It is neither a max nor a min nor a saddle point. It is a point of inflection. In fact, the function f(x,y) is identically zero along the line y=x. It is positive above that line and negative below it.